Solution Found!
Refer to Example 7.2. The amount of fill dispensed by a bottling machine is normally
Chapter 7, Problem 7.9(choose chapter or problem)
Refer to Example 7.2. The amount of fill dispensed by a bottling machine is normally distributed with = 1 ounce. If n = 9 bottles are randomly selected from the output of the machine, we found that the probability that the sample mean will be within .3 ounce of the true mean is .6318. Suppose that Y is to be computed using a sample of size n. a If n = 16, what is P(|Y | .3)? b Find P(|Y | .3) when Y is to be computed using samples of sizes n = 25, n = 36, n = 49, and n = 64. c What pattern do you observe among the values for P(|Y | .3) that you observed for the various values of n? d Do the results that you obtained in part (b) seem to be consistent with the result obtained in Example 7.3?
Questions & Answers
QUESTION:
Refer to Example 7.2. The amount of fill dispensed by a bottling machine is normally distributed with = 1 ounce. If n = 9 bottles are randomly selected from the output of the machine, we found that the probability that the sample mean will be within .3 ounce of the true mean is .6318. Suppose that Y is to be computed using a sample of size n. a If n = 16, what is P(|Y | .3)? b Find P(|Y | .3) when Y is to be computed using samples of sizes n = 25, n = 36, n = 49, and n = 64. c What pattern do you observe among the values for P(|Y | .3) that you observed for the various values of n? d Do the results that you obtained in part (b) seem to be consistent with the result obtained in Example 7.3?
ANSWER:Step 1 of 5
Given data:
The random variable Y follows the normal distribution with standard deviation 
If n = 9 bottles are randomly selected from the machine's output, it is found that the probability that the sample mean will be within 0.3 ounces of the true mean is 0.6318.